Answer
The intensity of the sound wave that reaches the ears of a person standing at a distance of 120 meters from the runway is $0.17~W/m^2$
Work Step by Step
We can write an expression for the intensity 5.0-m away:
$I_1 = \frac{P}{A}$
$I_1 = \frac{P}{4\pi~r_1^2}$
We can write an expression for the intensity 120-m away:
$I_2 = \frac{P}{A}$
$I_2 = \frac{P}{4\pi~r_2^2}$
We can divide the two equations to find $I_2$:
$\frac{I_2}{I_1} = \frac{\frac{P}{4\pi~r_2^2}}{\frac{P}{4\pi~r_1^2}}$
$I_2 = \frac{r_1^2}{r_2^2}~\times I_1$
$I_2 = \frac{(5.0~m)^2}{(120~m)^2}\times (1.0\times 10^2~W/m^2)$
$I_2 = 0.17~W/m^2$
The intensity of the sound wave that reaches the ears of a person standing at a distance of 120 meters from the runway is $0.17~W/m^2$.
